Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model

Abstract

Our mathematical model of epithelial transport (Larsen et al. Acta Physiol. 195:171–186, 2009) is extended by equations for currents and conductance of apical SGLT2. With independent variables of the physiological parameter space, the model reproduces intracellular solute concentrations, ion and water fluxes, and electrophysiology of proximal convoluted tubule. The following were shown: Water flux is given by active Na+ flux into lateral spaces, while osmolarity of absorbed fluid depends on osmotic permeability of apical membranes. Following aquaporin “knock-out,” water uptake is not reduced but redirected to the paracellular pathway. Reported decrease in epithelial water uptake in aquaporin-1 knock-out mouse is caused by downregulation of active Na+ absorption. Luminal glucose stimulates Na+ uptake by instantaneous depolarization-induced pump activity (“cross-talk”) and delayed stimulation because of slow rise in intracellular [Na+]. Rate of fluid absorption and flux of active K+ absorption would have to be attuned at epithelial cell level for the [K+] of the absorbate being in the physiological range of interstitial [K+]. Following unilateral osmotic perturbation, time course of water fluxes between intraepithelial compartments provides physical explanation for the transepithelial osmotic permeability being orders of magnitude smaller than cell membranes’ osmotic permeability. Fluid absorption is always hyperosmotic to bath. Deviation from isosmotic absorption is increased in presence of glucose contrasting experimental studies showing isosmotic transport being independent of glucose uptake. For achieving isosmotic transport, the cost of Na+ recirculation is predicted to be but a few percent of the energy consumption of Na+/K+ pumps.

Ion and Water Absorption by the Kidney Proximal Tubule: Computational Analysis of Isosmotic Transport

“…Here we briefly review a model of considerable explanatory power, which for the first time reveals what we believe is the precise mechanism by which basolateral sodium recirculation generates true isosmotic transport at an insignificant metabolic cost. 3 Our results open the way for testing the predictions of the model in future experimental work. The governing electrodiffusion equations in the model include current equations for the rheogenic Na + /K + pump and conductance equations for the luminal rheogenic sodium-glucose transporter SGLT2.…”

“… 5 When engaged in glucose absorption, the osmolarity of the emerging fluid is 335 mosM, thus deviating even more from isosmotic transport. 3 …”

“…FR apical is the ratio of apical (luminal) membrane resistance to transcellular resistance. 3 ( B ) Model solution illustrating how true isosmotic transport is obtained by recirculating Na + from the serosal compartment into the lateral intercellular compartment ( lis ). All independent variables are similar to those used in computations of Figure 1A in which the 1Na + :1Cl − cotransporter in serosal membrane is quiescent.…”

“…All independent variables are similar to those used in computations of Figure 1A in which the 1Na + :1Cl − cotransporter in serosal membrane is quiescent. 3 …”

“…With glucose uptake, the junctional leak fluxes are similarly predicted to be effectively eliminated by solvent drag, which generates a paracellular Na + flux of >600 pmol/(cm 2 s). 3 Because this component bypasses the lateral Na + /K + pump absorption of filtered fluid is energetically more efficient than predicted from the turnover of the lateral pump itself.…”